You can afford a $1200 per month mortgage payment. You've found a 30 year loan at 5.3% interest.

a) How big of a loan can you afford? (Round to the nearest cent, as needed.)

$


b) How much total money will you pay the loan company? (Round to the nearest cent, as needed.)

$


c) How much of that money is interest? (Round to the nearest cent, as needed.)


To answer these questions, we'll need to use the formula for the monthly payment on a mortgage loan:

\[
M = \frac{P \cdot r(1 + r)^n}{(1 + r)^n - 1}
\]

Where:
- $ M $ is the monthly mortgage payment ($1200 in this case).
- $ P $ is the loan principal (the amount you're borrowing, which we're solving for in part a).
- $ r $ is the monthly interest rate (annual interest rate divided by 12).
- $ n $ is the total number of payments (loan term in years multiplied by 12).

### a) How big of a loan can you afford?

Given:
- $ M = 1200 $
- $ r = \frac{5.3\%}{12} = \frac{0.053}{12} = 0.0044167 $
- $ n = 30 \times 12 = 360 $

We can rearrange the formula to solve for $ P $:

\[
P = \frac{M \cdot \left( (1 + r)^n - 1 \right)}{r(1 + r)^n}
\]

Plugging in the values:

\[
P = \frac{1200 \cdot \left( (1 + 0.0044167)^{360} - 1 \right)}{0.0044167 \cdot (1 + 0.0044167)^{360}}
\]

Let me calculate this.### a) The loan you can afford is approximately **$216,097.60**.

### b) How much total money will you pay the loan company?

The total amount paid over the life of the loan is the monthly payment multiplied by the total number of payments:

\[
\text{Total Payment} = M \times n = 1200 \times 360
\]

Let's calculate this.### b) The total amount of money you will pay the loan company is **$432,000**.

### c) How much of that money is interest?

The interest paid is the difference between the total amount paid and the loan principal:

\[
\text{Interest} = \text{Total Payment} - P
\]

Let's calculate this.### c) The total amount of interest you will pay is approximately **$215,902.40**.

Would you like more details or have any questions? Here are some related questions you might consider:

1. What would happen to the loan amount if the interest rate decreased by 1%?
2. How would a 15-year mortgage term affect the total interest paid?
3. What if you could afford a $1500 monthly payment instead?
4. How does the loan amount change with a different interest rate?
5. How does making an extra payment each year affect the total interest paid?

**Tip:** Paying extra toward the principal each month can significantly reduce the total interest paid over the life of the loan.

You can afford a $1200 per month mortgage payment. You've found a 30-year loan at 5.3% interest.
a) How big of a loan can you afford? (Round to the nearest cent, as needed.)

b) How much total money will you pay the loan company? (Round to the nearest cent, as needed.)

c) How much of that money is interest? (Round to the nearest cent, as needed.)

Learn how to calculate the maximum loan amount you can afford, total payment, and interest for a 30-year mortgage with a $1200 monthly payment at 5.3% interest. This guide uses key algebraic formulas suitable for students in Grades 10-12.

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